Natural Frequencies and Stability of a Spinning Disk Under Follower Edge Tractions

Abstract

The vibration and stability of a spinning disk under follower edge tractions are studied both numerically and analytically. The edge traction is circumferentially stationary in the space. When the compressive traction is uniform, natural frequencies of most of the non-reflected waves decrease, except some of the zero-nodal-circle modes with small number of nodal diameters in the low frequency range. When the spinning disk is under nonuniform traction in the form of cos kθ, where k is a nonzero integer, it is found that the eigenvalue only changes slightly under the edge traction if the natural frequency of interest is well separated from others. When two modes are almost degenerate, however, modal interaction (frequency loci veering or merging) occurs when the difference between the number of nodal diameters of these two modes is equal to ±k. Types of modal interaction vary as the radius ratio of the circular disk changes. Analytical methods for predicting how the eigenvalue changes and what type of modal interaction will occur are proposed and verified.